The reliability of electronic systems is critically dependent on robust solder joints in BGA components. This study evaluates Ball Grid Array (BGA) solder-joint reliability under controlled harmonic vibration loading conditions, highlighting the real-world mechanical stresses experienced by electronic systems. Recent research has focused on enhancing BGA reliability through design optimization. A sensitivity analysis assessed how variations in diameter and height affect BGA mechanical performance, using cycles to failure from vibration isothermal fatigue assessments as the key metric. A comprehensive investigation identified the optimal alloy for accurate fatigue law implementation, studying SAC105, SAC305, SAC405, and InnoLot alloys. Finite element analysis simulated solder joint behavior, revealing that InnoLot alloy exhibits a significantly longer lifespan than SAC alloys, demonstrating improved fatigue life, establishing it as the superior choice for reliability under harmonic excitation at 25 ℃. Further analysis showed that increased diameter and height correlate with higher cycles to failure, suggesting that larger solder joints enhance reliability. This study provides valuable insights for the electronics industry, facilitating optimal solder alloy selection and the establishment of ideal geometric parameters for future BGA component applications. Through targeted consideration of these factors, we aim to improve the durability and performance of electronic systems in real-world conditions.